Machine for calculating moments of inertia



May 22, 1928. 1,670,512

A." KORONSKI ET AL MACHINE FOR CALCULATING MOMENTS OF INERTIA Filed Nov. 27 920 5 Sheets-Sheet l 0 O O\ m v 98 O k 0 K u v Jo/zvr INVENTOIRS May 22, 1928.

A.. ORONSKI ET AL MACHINE FOR CALCULATING MOMENTS OF INERTIA Filed Nov. 271 1920 3 Sheets-Sheet FiqfZ Cr-o ss Sec/f 4,4

Jonvr INVENTORS May 22, 1928.

A. KORONSKI ET AL MACHINE FOR CALCULATING MOMENTS 0F INERTIA Filed Nov. 27 1920 3 Sheets-Sheet Patented May 22, 1928.

UNITED ANDRE KORON SKI, OF'NARBEBTH, AND RALPH HEACOCK, OF SWAR-TI-IMOBE, TENN- SYLVANIA; SAID ANDRE-KORONSKI NOW BY JUDICIAL CHANGE OE NAME ANDREW KING;

MACHINE-FOB CALCULATING MOMENTS OF INEBTIA;

Application filed November 27, 1920. Serial No. 426,791.

Our invention relates to machines for calculating' moments of inertia graphically and by means of this machine the calculator can seealmost at a glance the eiiect on the moment of-inertiaof any change-inshapeof the area being calculated and the moment ofinertia ofirregul'ar shapes can be' determined quickly and with greaterfaccuracy than'ris 113; possible except by very laborious metho For educational p'urp'osesthis machine'h'as the advantage that it presentst'he moment of inertia graphically in such a' way that its relation totheareaof'which the moment of inertia is bein calculated can be clearly seen, thus enab ing'thestudent to grasp'this relation more readily, a thing which' isve'ry dillicult to do without such help.

. The objects of this, invention are to provide a simple-meansio'f obtaining moments of inertia: mechanically and, also to make a graphical representation of them.

We attain these objects by means of the construction described in the annexed spect- 26 fi cation and shown in the accompanying drawings and in which;

Fig; 1' is an isometric view of the device. Fig.- 2 shows the surface of the drum 20 developed.

Fig. 3 is a section thruthe end of the drum the pingvas will be explained later chine' showing the relativepositionof the various parts.

Fig. 5 is a longitudinal section thru the machine along'the center of'the axle 10.

6 is an endiview' of Fig. 3. Referring to Figs; 1" and 5', 1' and 2- are end frames intowhichar'e rigidly attached theyb'ars' 3, 4, 5 andifithe' whole forming the rigid carriage? Pivoted in thisca'rri'a' e' by means of the screws 8 and 9 is the ax e10 which is provided with'the'zpoints' 11? and 12 whichbearfin the conicalholes in the ,screws'S and 9 as shown in Fig. 5 These screws are provided withl'ock-nuts 13' and Rigidly attached'to the axle, are the two knurled wheels 15 and l6 on which thec'arriage 7 ridesand'by'which it is constrained =l7 is P dto balance the carriage 7 Pivoted on'the axle'10, by means of" the disks 18 and 19, isthe drum 2O Whichis rigidly attached to the said disks. Motion along the axle 10 is prevented by the collars 21 and 22 which are attached to the said'axle by, means of set screws; 4

Riding on the bars 3, 4, 5 andi6'are the carriages 23 and 24, of which 23 is provided with the-pointer 25 and a carriage gripq 26 for operating the device, and 24 is provide 7 with the" pencil 27.

In order to eliminate friction, these carriag-es are provided withvarious/rollers 28,

29, 30, 31 and32 as shown, and some ofthese rollers are adjustable so as to take-up the play between said rollers and the bars on which they ride.

The carriages=23 and 24' are also-provided withpins 33 and 34 respectively,- which engage-grooves on the drum 20 as will be described later.

On the face of the drum 20are cut the grooves 35, 36 and-37 as shown,fideveloped diagrammatically, in F ig. 2. The curve 35 is a helix and this-is engaged by thepin33.

The curve 36 is equalto and thefcurve 37 isequal to "either of which may en- The pins 33and 34 are placed on-diametrically o posite sides of thedrum 2O and the helix 3 is so placed relative to the curves 36 and 37 that'the pin 33 engages the helix on one side of thedrum 20 while the pin 34 is engaged by whichever of the curves 36 or 37' it is desired 'touse on the otherside.

I It. willbe noted that if the carriage 23 is moved parallel tothe axis of the drum 20 the pin33 riding in the helix 35 will cause said drum to revolve and the curve 36 (or 37 )by engaging the pin 34 will cause the carriage 24 to move in a direction parallel tg the axis of. the drum a distance 'equalto 3 (or where :v is the distance traveled by thecar'riage23. I

If the carriage 23 is moved at right langles .willbeequalto the moment ofinertia of the revolve and the distance traveled by the pencil 27 is equal to the distance traveled by the pointer 25.

The moments of inertia of a rectangular area about an axis drawn thru its-base 1s 3 equal to where b is its breadth and d is the distance from the said axis to the upper edge. Irregular areas may be divided into a. large number of rectangles similar to the above and the sum of the moments of inertia of these areas is equal to the moment of inertia. of the area in question.

From the above, it will be seen that if the area be traced with the tracer point, the penv cil 27 will'trace a figure the area of which (as determined by a planimeter or otherwise) multiplied by ten if the curve is used, or by twenty if the; curve gis used,

giVen area about the given axis. 1

This area may be determined independ- .;ently'(by planimeter or Otherwise) if ithas been drawn by the pencil 27 or, if aplanimeter tracer point is pivotally attached to .the pencil carriage-24, the area of this figure may be determined at the same time that it is being drawn.

- The two curves 36 and 37 are provided to insure greater accuracy for calculating a greater range of areas than could be determined if only one curve were provided.-- The curve 37 is for; use when moments of inertia oflarge areas are to be determined and the curve 36 is for small areas.

We have shown the machine as made with a drum 20 which is rotated by the motion of the carriage 23 and which drives the carriage 24' but the same result can be obtained by using a disc instead of the drum and we therefore do not wish to limit ourselves to the construction shown herein as we believe that the idea of obtaining graphically by mechanical means the relation between an area and its moment of inertia is new.

We are aware that prior to this invention machines for calculating moments of inertia have been made which represent the moment of inertia graphically. We therefore do not claim such a device broadly but We claim: I 1. In combination, a main carriage provided with means for rolling in a direction atright angles to its axis while remaining parallel to it, a drum pivoted in this main. carriage with its axis parallel to the axis of said carriage but capable of rotating independently of the motion of said carriage, a helical groove cut into the face 'of'said drum, .a small carriage capable of moving freely on the main carriage in a direction parallel to the axis of said drum, a pin attached to said small carriage and engaging the helical groove in said drum in such a manner that motion of the small carriage rotates the said drum thru the medium of the said pin, a pointer attached to'said small carriage for tracing over-areas of which the moment of inertia is to be determined, a second small carriage also capable of moving on the main carriage parallel tolthe axis of said drum, a second pin attached to said,

second small carriage which engages a second curved groove cut into said drum (the equation ofsaid curved groove being the second small carriage being driven propor- 3 tionately to by the motion ofsaid 'drum thru the medium of the second pin and means for recording the motion of said sec- 0nd small carriage 1 2. The combination of means for tracing around an area, themoment of inertia-50f which is to be determ1ned;.a' member capable of being operated by said tracing means and a drawing member I capable .of being driven by the tracing means thru the medium-of said first named memberto cause the second named member to move in such.v a

way that its ordinates are proportional to the cube of the ordinates of the movement of said tracing means. i .y 7

3. In combinatioma tracer point, a pencil and means'including a drum on which are cut suitable curved grooves whereby the motion of said tracer point causes the said pencil to draw an area proportionate to the mo ment of inertia of the area traced by said tracer point.

4. In combination, a tracer po1nt, a carriage carrying said tracer point, a pin carried bysaid carriage,a rotatable cylinder in the face of which a helical grooveiis cut which is engaged bysaid pin and by:which said cylinder may be rotated, a groove whose equation is that of a cubical curve cut into the said cylinder similarly to the helix,

a second pin engaging said groove whose equation is that of a cubical curve, a second carnage carrylng sald second pin and thru tracer whereby the ordinate drawn by the and drawing means whereby movement of point and the tracer are in the relation of said tracing means in a given direction 3 causes said drawing means to move propor- 10 7 tienate1y to the cube of the movement of 5 6. Means for calculating the moment of Sand tracmg means- ,7

inertia comprising tracing means, drawing ANDRE KORONSKI. means and means intermediate said traeing RALPH H. HEACOCK.

y: and the abscissae are equal. 

